e m LimiteanleTpdf E Openwitheaoglexs - Chapter 1 1, Use the NT to show that at any fixed time, on a great circle on the surface of the earth, there is always a pair of points at the opposite ends of a diameter that are at the same temperature. Hint: Consider the function that represents the temperature differential between opposite ends of a diameter along a great circle of Earth, idea T(x) = Tern p(position1) Temp(position2) 2. Complete Exercise 108 on page 81. 3. Find two functions, f(x) and g(x), such that all three of the following conditions are true: lim f(x) does not exist xiD icing g(x) does not exist $3309) + 9(1)) does exit S() for x # c and f(c) + g(c), then either for g is not continuous at c. 105. A rational function can have infinitely many x-values at which it is not continuous. 106. The function f(x) = 1x - 11 X - is continuous on (-0o, oo). 107. Think About It Describe how the functions f(x) = 3 + [x] and g(x) = 3 - [-x] differ. 108. HOW DO YOU SEE IT? Every day you dissolve 28 ounces of chlorine in a swimming pool. The graph shows the amount of chlorine f (t) in the pool after t days. Estimate and interpret lim f(t) and lim f(t). 1-4+ 140 112 84- 56 28 109. Telephone Charges A long distance phone service charges $0.40 for the first 10 minutes and $0.05 for each additional minute or fraction thereof. Use the greatest integer function to write the cost C of a call in terms of time t (in minutes). Sketch the graph of this function and discuss its continuity. 110. Inventory Management . . The number of units in inventory in a small company is given by N(1) - 25 ( 2 # 7 2 -1 ) where t is the time in months. Sketch the graph of this function and discuss its continuity